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Реферат: Вычислительная техника в управлении на примерре управления международных связей ВГУЭС.
Вычислительная техника в управлении на примерре управления международных связей ВГУЭС.
Gi?(V,X) ?en. 1 Caaa?a1 Aey iai?eaioe?iaaiiiai a?aoa G, annioee?iaaiiiai n a?aoii Gi? auienaou (ia?aioia?iaaa aa?oeiu) : a) iii?anoai aa?oei V e iii?anoai ?aaa? X, G(V,X); a) nienee nia?iinoe; a) iao?eoo eioeaaioiinoe; a) iao?eoo aania. a) Aey a?aoa Gi? auienaou iao?eoo nia?iinoe. Ioia?aoey aa?oei - ni. ?en 1 a) V={0,1,2,3,4,5,6,7,8,9} X={{0,1},{0,2},{0,3},{1,2},{1,4},{1,5},{1,6},{1,7},{2,3},{2,5},{3,8},{3,9},{4,5},{4,6},{5,3},{5,6},{5,8},{6,9},{7,8},{7,9},{8,9}} A aaeuiaeoai ?aa?a aoaoo iaicia?aouny iiia?aie a oeacaiiii ii?yaea ia?eiay n ioey. a) A0={1,2,3}; A1={0,2,4,5,6,7}; A2={0,1,3,5}; A3={0,2,5,8,9}; A4={1,5,6}; A5={1,2,3,4,6,8}; A6={1,4,5,9}; A7={1,8,9}; A8={1,3,5,7,9}; A9={3,6,7,8}; a) Ioia?aoey aa?oei e ?aaa? niioaaonoaaiii i. a) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0
3 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 0 0
4 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0
5 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0
6 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0
7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0
8 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1
9 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1
a) Iieacaia aa?oiyy iieiaeia iao?eou, o.e. iao?eoa aania iai?eaioe?iaaiiiai a?aoa neiiao?e?ia ioiineoaeuii aeaaiie aeaaiiaee. 0 1 2 3 4 5 6 7 8 9
0
8 3 5
1
1
2 2 4 5
2
2
5
3
1
1 6
4
4 2
5
2
1
6
2
7
1 1
8
6
9
a) Iao?eoa nia?iinoe aey a?aoa Gi?. 0 1 2 3 4 5 6 7 8 9
0
1 1 1
1 -1
1
1 1 1 1
2 -1 -1
1
1
3 -1
-1
-1
1 1
4
-1
1 1
5
-1 -1 1 -1
1
1
6
-1
-1 -1
1
7
-1
1 1
8
-1
-1
-1
1
9
-1
-1 -1 -1
Caaa?a 2 Iaeoe aeaiao? D(G), ?aaeon R(G), eiee?anoai oaio?ia Z(G) aey a?aoa G ; oeacaou aa?oeiu, yaey?ueany oaio?aie a?aoa G. D(G)=2 R(G)=2 Z(G)=10 Ana aa?oeiu a?aoa G(V,X) yaey?ony oaio?aie. Caaa?a 3 Ia?aioia?iaaou aa?oeiu a?aoa G, eniieucoy aeai?eoiu: a) "iienea a aeoaeio"; a) "iienea a oe?eio". Enoiaiay aa?oeia - . a) a) Caaa?a 4 Eniieucoy aeai?eoi I?eia iaeoe inoia ieieiaeuiiai aana a?aoa G. auienaou eia oeeaaee ia ieineinoe iaeaaiiiai aa?aaa, i?eiya ca ei?iaao? aa?oeio . Aan iaeaaiiiai aa?aaa - 14. Eia oeeaaee aa?aaa: 000011000001111111. Caaa?a 5 Eniieucoy aeai?eoi Aaeeno?a iaeoe aa?ai e?ao?aeoeo iooae ec aa?oeiu a?aoa G. Aan iaeaaiiiai iooe - 8. Caaa?a 6 Eniieucoy aeai?eoi Oi?aa - Oaeea?niia, iaeoe iaeneiaeuiue iioie ai acaaoaiiie aaoiie?niie i?eaioe?iaaiiie naoe {Gi? , , w}. Oeacaou ?ac?ac ieieiaeuiiai aana. Iineaaiaaoaeuiinou ianuuaiey naoe (ianuuaiiua ?aa?a ioia?aiu e?o?a?eaie): 1-e oaa 2-e oaa 3-e oaa 4-e oaa 5-e oaa 6-e oaa 7-e oaa Ieii?aoaeuii eiaai: Eae aeaii ec ?enoiea, ?aa?a {6,9},{7,9},{3,9}, ieoa?uea aa?oeio , ianuuaiiu, a inoaaoaany ?aa?i {8,9}, ieoa?uaany io aa?oeiu 8, ia ii?ao iieo?eou aieuoaa cia?aiea aaniaie ooieoee, oae eae ianuuaiiu ana ?aa?a, ieoa?uea aa?oeio 8. A?oaeie neiaaie - anee ioa?ineou ana ianuuaiiua ?aa?a, oi aa?oeia iaainoe?eia, ?oi yaeyaony i?eciaeii iaeneiaeuiiai iioiea a naoe. Iaeneiaeuiue iioie a naoe ?aaai 12. Ieieiaeuiue ?ac?ac naoe ii ?eneo ?aaa?: {{0,1},{0,2},{0,3}}. Aai i?iioneiay niiniaiinou ?aaia 16 Ieieiaeuiue ?ac?ac naoe ii i?iioneiie niiniaiinoe: {{6,9}, {7,9}, {3,9}, {3,8}, {5,8}, {7,8}}. Aai i?iioneiay niiniaiinou ?aaia 12. Caaa?a 7 (Caaa?a i ii?oaeuiia) Auienaou noaiaiio? iineaaiaaoaeuiinou aa?oei a?aoa G. a) Oeacaou a a?aoa G Yeea?iao oaiu. Anee oaeiaie oaie ia nouanoaoao, oi a a?aoa G aiaaaeou iaeiaiuoaa ?enei ?aaa? oaeei ia?acii, ?oiau a iiaii a?aoa ii?ii auei oeacaou Yeea?iao oaiu. a) Oeacaou a a?aoa G Yeea?ia oeee. Anee oaeiai oeeea ia nouanoaoao, oi a a?aoa G aiaaaeou iaeiaiuoaa ?enei ?aaa? oaeei ia?acii, ?oiau a iiaii a?aoa ii?ii auei oeacaou Yeea?ia oeee. Noaiaiiay iineaaiaaoaeuiinou aa?oei a?aoa G: (3,6,4,5,3,6,4,3,4,4) a) Aey nouanoaiaaiey Yeea?iaie oaie aiionoeii oieuei aaa aa?oeiu n ia?aoiuie noaiaiyie, iiyoiio iaiaoiaeii aiaaaeou iaii ?aa?i, nea?ai ia?ao aa?oeiaie 4 e 7. Iieo?aiiay Yeea?iaa oaiu: 0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3. Noaia Yeea?iaie oaie (aiaaaeaiiia ?aa?i iieacaii ioieoe?ii): a) Aiaeiae?ii ioieoo a) aiaaaeyai ?aa?i {3,0}, caiueay Yeea?iao oaiu (i?e yoii auiieiyy oneiaea nouanoaiaaiey Yeea?iaa oeeea - ?aoiinou noaiaiae anao aa?oei). ?aa?i {3,0} e?aoiia, ?oi ia i?ioeai?a?eo caaaie?, ii i?e iaiaoiaeiinoe ii?ii aaanoe ?aa?a {0,7} e {4,3} aianoi ?aiaa aaaaaiiuo. Iieo?aiiue Yeea?ia oeee: 0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3,0. Noaia Yeea?iaa oeeea (aiaaaeaiiua ?aa?a iieacaiu ioieoe?ii): Caaa?a 8 a) Oeacaou a a?aoa Gi? Aaieeuoiiia ioou. Anee oaeie ioou ia nouanoaoao, oi a a?aoa Gi? eciaieou i?eaioaoe? iaeiaiuoaai ?enea ?aaa? oaeei ia?acii, ?oiau a iiaii a?aoa Aaieeuoiiia ioou ii?ii auei oeacaou. a) Oeacaou a a?aoa Gi? Aaieeuoiiia oeee. Anee oaeie oeee ia nouanoaoao, oi a a?aoa Gi? eciaieou i?eaioaoe? iaeiaiuoaai ?enea ?aaa? oaeei ia?acii, ?oiau a iiaii a?aoa Aaieeuoiiia oeee ii?ii auei oeacaou. a) Aaieeuoiiia ioou (?aa?a n eciaiaiiie i?eaioaoeae iieacaiu ioieoe?ii): a) Aaieeuoiiia oeee (?aa?a n eciaiaiiie i?eaioaoeae iieacaiu ioieoe?ii): Caaa?a 9 (Caaa?a i eiiieaiy?a?a) Aai iieiue i?eaioe?iaaiiue neiiao?e?aneee a?ao n aa?oeiaie x1, x2,...xn.Aan aoae xixj caaai yeaiaioaie Vij iao?eou aania. Eniieucoy aeai?eoi iaoiaa aaoaae e a?aieo, iaeoe Aaieeuoiiia eiioo? ieieiaeuiiai (iaeneiaeuiiai) aana. Caaa?o ia iaeneiaeuiia cia?aiea Aaieeuoiiiaa eiioo?a naanoe e caaa?a ia ieieiaeuiia cia?aiea, ?anniio?aa iao?eoo n yeaiaioaie ,aaa . Auiieieou ?enoiie. Enoiaiay oaaeeoa. x1 x2 x3 x4 x5 x6
x1
3 7 2
11
x2 8
06
4 3
x3 6 05
7
2
x4 6
13
5
x5 3 3 3 4
5
x6 8 6
2 2
Oaaeeoa A 14 x1 x2 x3 x4 x5 x6
x1
1 5 01
7 2
x2 8
01
4 1
x3 6 00
7
00
x4 1
8
01
5
x5 01 00 00 1
00 3
x6 6 4
00 00
2
2
A?iaei ii ia?aoiao x2-x3: Oaaeeoa 23 =14+0=14 x1 x2 x4 x5 x6
x1
1 01
7
x3 6
7
06
x4 1
01
x5 01 01 1
00
x6 6 4 00 00
Oaaeeoa 23 =14+1=15 x1 x2 x3 x4 x5 x6
x1
1 5 01
7
x2 7
3 03 1
x3 6 00
7
00
x4 1
8
01
x5 01 00 05 1
00
x6 6 4
00 00
I?iaie?aai ii 23. A?iaei ii ia?aoiao x3-x6: Oaaeeoa 23E36 =14+0=14 x1 x2 x4 x5
x1
1 01
x4 1
01
x5 01 01 1
x6 6
00 00
Oaaeeoa 2336 =14+6=20 x1 x2 x4 x5 x6
x1
1 01
7
x3 01
1
6
x4 1
01
x5 00 01 1
07
x6 6 4 00 00
I?iaie?aai ii 2336. A?iaei ii ia?aoiao x4-x5: Oaaeeoa 23E3645 =14+0=14 x1 x2 x4
x1
1 01
x5 01 01 1
x6 6
00
Oaaeeoa 233645 =14+1=15 x1 x2 x4 x5
x1
1 01
x4 00
1
x5 01 01 1
x6 6
00 00
I?iaie?aai ii 233645. A?iaei ii ia?aoiao x5-x1: Oaaeeoa 23364551 =14+1=15 x2 x4
x1 1
1
x6
00
Oaaeeoa 23364551 =14+6=20 x1 x2 x4
x1
1 01
x5
01
x6 0
00
6
Ieii?aoaeuii eiaai Aaieeuoiiia eiioo?: 2,3,6,4,5,1,2. I?aaa?aai ?acaeaiee: Caaa?a 10 (Caaa?a i iacia?aieyo) Aai iieiue aaoaieuiue a?ao Knn n aa?oeiaie ia?aie aiee x1, x2,...xn.e aa?oeiaie a?oaie aiee y1, y2,...yn..Aan ?aa?a {xi,yj} caaaaony yeaiaioaie vij iao?eou aania. Eniieucoy aaiaa?neee aeai?eoi, iaeoe niaa?oaiiia ia?ini?aoaiea ieieiaeuiiai (iaeneiaeuiiai aana). Auiieieou ?enoiie. Iao?eoa aania aaoaieuiiai a?aoa K55 : y1 y2 y3 y4 y5
x1 2 0 0 0 0
x2 0 7 9 8 6
x3 0 1 3 2 2
x4 0 8 7 6 4
x5 0 7 6 8 3
Ia?aue yoai - iieo?aiea ioeae ia io?ai, o. e. ioee o?a anou ai anao no?ie e noieaoao. Aoi?ie yoai - iaoi?aaiea iieiiai ia?ini?aoaiey. y1 y2 y3 y4 y5 x1 2 0 0 0 0
x2 0 7 9 8 6
x3 0 1 3 2 2
x4 0 8 7 6 4
x5 0 7 6 8 3
O?aoee yoai - iaoi?aaiea iaeneiaeuiiai ia?ini?aoaiey. y1 y2 y3 y4 y5
x1 2 0 0 0 0 X
x2 0 7 9 8 6 X
x3 0 1 3 2 2
x4 0 8 7 6 4
x5 0 7 6 8 3
X X
?aoaa?oue yoai - iaoi?aaiea ieieiaeuiie iii?u. y1 y2 y3 y4 y5
x1 2 0 0 0 0
x2 0 7 9 8 6 5
x3 0 1 3 2 2 1
x4 0 8 7 6 4 2
x5 0 7 6 8 3 3
4
Iyoue yoai - aicii?iay ia?anoaiiaea iaeioi?uo ioeae. y1 y2 y3 y4 y5
x1 3 0 0 0 0
x2 0 6 8 7 5 5
x3 0 0 2 1 1 1
x4 0 7 6 5 3 2
x5 0 6 5 7 2 3
4
?aoaiea n iaioeaaui cia?aieai. Ia?aoia ei aoi?iio yoaio. Iieiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 3 0 0 0 0
x2 0 6 8 7 5
x3 0 0 2 1 1
x4 0 7 6 5 3
x5 0 6 5 7 2
Iaeneiaeuiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 3 0 0 0 0 X
x2 0 6 8 7 5 X
x3 0 0 2 1 1
x4 0 7 6 5 3
x5 0 6 5 7 2
X X
Ieieiaeuiay iii?a: y1 y2 y3 y4 y5
x1 3 0 0 0 0 6
x2 0 6 8 7 5 7
x3 0 0 2 1 1 1
x4 0 7 6 5 3 2
x5 0 6 5 7 2 3
4 5
Ia?anoaiiaea ioeae: y1 y2 y3 y4 y5
x1 3 0 0 0 0 6
x2 0 6 8 7 5 7
x3 0 0 2 1 1 1
x4 0 7 6 5 3 2
x5 0 6 5 7 2 3
4 5
Iieiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 3 0 0 0 0 6
x2 0 6 8 7 5 7
x3 0 0 2 1 1 1
x4 0 7 6 5 3 2
x5 0 6 5 7 2 3
4 5
Iaeneiaeuiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 3 0 0 0 0 X
x2 0 6 8 7 5
x3 0 0 2 1 1 X
x4 0 7 6 5 3 X
x5 0 6 5 7 2
X X X
Ieieiaeuiay iii?a: y1 y2 y3 y4 y5
x1 3 0 0 0 0
x2 0 6 8 7 5 1
x3 0 0 2 1 1
x4 0 7 6 5 3
x5 0 6 5 7 2 2
3
Ia?anoaiiaea ioeae: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3 1
x3 2 0 2 1 1
x4 2 7 6 5 3
x5 0 4 3 5 0 2
3
Iieiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3
x3 2 0 2 1 1
x4 2 7 6 5 3
x5 0 4 3 5 0
Iaeneiaeuiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 5 0 0 0 0 X
x2 0 4 6 5 3 X
x3 2 0 2 1 1 X
x4 2 7 6 5 3
x5 0 4 3 5 0 X
X X X
X
Ieieiaeuiay iii?a: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3
x3 2 0 2 1 1
x4 2 7 6 5 3 1
x5 0 4 3 5 0
Ia?anoaiiaea ioeae: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3
x3 2 0 2 1 1
x4 0 5 4 3 1 1
x5 0 4 3 5 0
Iieiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3
x3 2 0 2 1 1
x4 0 5 4 3 1 1
x5 0 4 3 5 0
Iaeneiaeuiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 5 0 0 0 0 X
x2 0 4 6 5 3 X
x3 2 0 2 1 1 X
x4 0 5 4 3 1
x5 0 4 3 5 0 X
X X X
X
Ieieiaeuiay iii?a: y1 y2 y3 y4 y5
x1 5 0 0 0 0
x2 0 4 6 5 3 3
x3 2 0 2 1 1
x4 0 5 4 3 1 1
x5 0 4 3 5 0
2
Ia?anoaiiaea ioeae: y1 y2 y3 y4 y5
x1 6 0 0 0 0
x2 0 3 5 4 2 3
x3 3 0 2 1 1
x4 0 4 3 2 0 1
x5 1 4 3 5 0
2
Iieiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 6 0 0 0 0
x2 0 3 5 4 2 3
x3 3 0 2 1 1
x4 0 4 3 2 0 1
x5 1 4 3 5 0
2
Iaeneiaeuiia ia?ini?aoaiea: y1 y2 y3 y4 y5
x1 6 0 0 0 0 X
x2 0 3 5 4 2 X
x3 3 0 2 1 1 X
x4 0 4 3 2 0
x5 1 4 3 5 0 X
X X X
X
Ieieiaeuiay iii?a: y1 y2 y3 y4 y5
x1 6 0 0 0 0
x2 0 3 5 4 2 4
x3 3 0 2 1 1
x4 0 4 3 2 0 1
x5 1 4 3 5 0 5
2
3
A ?acoeuoaoa eiaai: y1 y2 y3 y4 y5
x1 6 0 0 0 0
x2 0 1 3 2 2 4
x3 3 0 2 1 1
x4 0 2 1 0 0 1
x5 1 4 3 5 0 5
2
3
Enoiaiue a?ao Iieo?aiiue a?ao: Aan iaeaaiiiai niaa?oaiiiai ia?ini?aoaiey = 12. Caaa?a 11 ?aoeou caaa?o 10, eniieucoy aeai?eoi aaoaae e a?aieo (ioi?aanoaea aa?oeiu xi e yj). Oaaeeoa A (enoiaiay). No?iee - xi , noieaou - yj. =0 1 2 3 4 5
1 2 01 03 02 02
2 06 7 9 8 6
3 01 1 3 2 2
4 04 8 7 6 4
5 03 7 6 8 3
A?iaei ii ia?aoiao x2 - y1: Oaaeeoa A21 =0+8=8 2 3 4 5
1 00 02 01 00
3 01 2 1 1 1
4 4 3 2 02 4
5 4 3 5 03 3
Oaaeeoa 21 =0+6=6 1 2 3 4 5
1 2 01 03 02 00
2
1 3 2 01 6
3 01 1 3 2 2
4 04 8 7 6 4
5 03 7 6 8 3
I?iaie?aai ii 21: A?iaei ii ia?aoiao x4 - y1: Oaaeeoa 21A41 =6+4=10 2 3 4 5
1 00 02 01 00
2 1 3 2 01
3 01 2 1 1 1
5 4 3 5 03 3
Oaaeeoa 2141 =6+4=10 1 2 3 4 5
1 2 01 03 02 00
2
1 3 2 01
3 01 1 3 2 2
4
4 3 2 02 4
5 03 7 6 8 3
I?iaie?aai ii A21: A?iaei ii ia?aoiao x5 - y5: Oaaeeoa A21A55 =8+2=10 2 3 4
1 00 01 00
3 01 2 1
4 2 1 01 2
Oaaeeoa A2155 =8+3=11 2 3 4 5
1 00 02 01 00
3 01 2 1 1
4 4 3 2 02
5 1 01 2
3
I?iaie?aai ii A21A55: A?iaei ii ia?aoiao x3 - y2: Oaaeeoa A21A55A32 =10+0=10 3 4
1 01 00
4 1 01
Aaeaa ?aoaiea i?aaeaii: x1 - y3 e x4 - y4. Yoi ia oaaee?eo ioaieo. A eoiaa eiaai niaa?oaiiia ia?ini?aoaiea n ieieiaeuiui aanii: I?aaa?aai ?acaeaiee:
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